Question

Find the 20 th term in the following sequence whose n th term is

Answer 1

The n th term of the sequence is given as,

a n = a n−1 n (1)

And it is given that a 1 =−1.

Substitute n=2 in equation (1),

a 2 = a 2−1 2 = a 1 2 = −1 2

Substitute n=3 in equation (1),

a 3 = a 3−1 3 = a 2 3 = −1 2 3 =− 1 6

Substitute n=4 in equation (1),

a 4 = a 4−1 4 = a 3 4 = −1 6 4 =− 1 24

Substitute n=5 in equation (1),

a 5 = a 5−1 5 = a 4 5 = −1 24 5 =− 1 120

The required first five terms are −1,− 1 2 ,− 1 6 ,− 1 24 ,− 1 120 .

The corresponding series will be,

( −1 )+( − 1 2 )+( − 1 6 )+( − 1 24 )+( − 1 120 )+⋯